On 11/6/2014 9:08 PM, Bruce Kellett wrote:
LizR wrote:
(Another way to look at this is that the expansion is producing more available states
for the universe to move into, effectively raising the entropy ceiling. This means an
expanding universe can never reach a state of equilibrium - this is particularly clear
during the BB fireball, which I would say is very near to equilibrium for a lot of the
time.)
I thought I remembered that someone had written that the idea that the expansion
produces more states so the entropy ceiling increases with the expansion of the universe
is mistaken. I have found the reference, it is Roger Penrose in 'The Road to Reality' in
Section 27.6 (p. 701ff)
He writes:
"There is a common view that the entropy increase in the second law is somehow just a
necessary consequence of the expansion of the universe. This opinion seems to be based
on the misunderstanding that there are comparatively few degrees of freedom available to
the universe when it is 'small', providing some kind of low 'ceiling' to possible
entropy values, and more available degrees of freedom when the universe gets larger,
giving a higher 'ceiling', thereby allowing higher entropies. ...
"There are many ways to see that this viewpoint cannot be correct....
...The degrees of freedom that are available to the universe are described by the total
phase space. The dynamics of GR (which include the degree of freedom defining the
universe's size) is just as much described by the motion of our point x in the phase
space as are all the other physical processes involved. This phase space is just
'there', and it does not in any sense 'grow with time', time not being part of the phase
space.
No, but dynamics consist of moving through phase space. Entropy is always relative to
constraints (with no constraints you just have the micro state and entropy is zero). So
relative to a given size I think the number of states does grow with size. Penrose is
right but he's removing the constraint on size.
Brent
There is no 'ceiling', because all states that are dynamically accessible to the
universe (or family of universes) under consideration must be represented in this phase
space....."
I recommend Penrose's book for a lucid explanation of these things.
Bruce
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